The coupled cluster method

Abstract

The coupled cluster method (CCM) is nowadays widely recognised as providing one of the most powerful, most universally applicable, and numerically most accurate at attainable levels of implementation, of all available ab initio methods of microscopic quantum many-body theory. The number of successful applications of the method to a wide range of physical and chemical systems is impressively large. In almost all such cases the numerical results are either the best or among the best available. A typical example is the electron gas, where the CCM results for the correlation energy agree over the entire metallic density range to within less than one millihartree per electron (or <1%) with the essentially exact Green?s function Monte Carlo results. What has since become known as the normal (NCCM) version of the method was invented some forty years ago to calculate the ground-state energies of closed-shell atomic nuclei. Extensions of the CCM have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from embedding linear response theory within the NCCM. Further extensions deal with the general dynamics of quantum many-body systems, and with their mixed states appropriate, for example, to their behaviour at nonzero temperatures. More recently, a so-called extended (ECCM) version of the method has been introduced. It has the same ability as the NCCM to describe accurately the local properties of quantum many-body systems, but it also has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. The role of the CCM within modern quantum many-body theory is first surveyed, by a comparison with, and discussion of, the alternative microscopic formulations. We then discuss the method and each of its individual components in considerable detail. Our overall aim is to stress the broad applicability of the method. To that end we introduce and exploit a very general theoretical framework in which to formulate the key ideas and to develop the theory. We end with a brief review of the applications of the method to date.